The United Auto Workers and the International Association of Machinists, faced with a troubled economy and tougher opposition from big business, are considering a shotgun marriage.

Such a union between the longtime rivals for the nation's transportation equipment manufacturing jobs could become the largest single organization of industrial workers in American history.

"It's only natural that we should get together," said George Poulin, a vice president of the 917,216-member IAM. "In this day of big business conglomerates, labor has to deal from strength. We continue as two competing internationals."

Proposals to merge with the IAM, "will be given serious consideration by this union," said Don Stillman, a spokesman for the 1.35-million-member UAW, which lost an estimated 230,000 members in the recent recession. He said both unions have appointed merger discussion committees that are expected to begin working within the next few weeks.

A UAW-IAM merger would be in keeping with the dreams of many labor leaders who have called for American workers to come together under one institutional roof. Those dreams led to the creation of the American Federation of Labor in 1881, the Congress of Industrial Organizations in 1935, and the merger of those groups into the AFL-CIO in 1955.

But the dream of labor "solidarity" has often been deferred by petty personal rivalries, real ideological differences and difficult administrative problems. Most labor sources agree that the UAW-IAM discussions will be marked by similar strains.

"Merging unions is as difficult as trying to get two religious denominations together. It's not so much a question of theology as it is a question of the bishops," said Russell W. Gibbons, a spokesman for the 1.2-million-member United Steelworkers of America, which has been seeking a merger with the 20,000-member Insurance Workers International Union.

In the case of the UAW and the IAM, Gibbons said, "You're not dealing with two bishops. You're dealing with two popes."

The "popes" are UAW President Douglas A. Fraser and IAM President William W. Winpisinger, two labor leaders known for their independence and strong, sometimes conflicting, opinions. One of the two probably would have to settle for the second-place position of secretary-treasurer in any combined union.

There is also the question of affiliation with the AFL-CIO. The IAM is a member of the federation, which the UAW broke away from in 1967. Now, AFL-CIO President Lane Kirkland has invited the UAW to rejoin the fold. a

Some labor leaders say that a UAW-IAM merger could facilitate the UAW's reentry into the federation. But others speculate that the combination could instead influence Winpisinger to break away from the federation. The IAM recently decided to leave the federation's Industrial Union Department in a despute over presidential endorsements. The defection will cost the IUD $270,000 in annual dues from the IAM.

Still, UAW and IAM sources say Fraser and Winpisinger believe their unions can do more together than they can do separately in checking employment and political losses. Business leaders, such as those at the U.S. Chamber of Commerce, agree.

"Clearly, a merged union would be tougher in terms of collective bargaining," said John Tysse, the chamber's labor law director. "You would expect a UAW-IAM unit to be more agressive along this line."

Tysse added that he believes the merger talk is the product of "a changing economic and political environment" in whch the unions "are losing some of their clout."

"There's no question that the national business community is increasing its sophistication [in checking organized labor], particularly in the governmental arena . . . Many of the techniques we're using to develop that sophistication were learned from the unions themselves," Tysse said.

Partly in an attempt to answer that chanllenge, 10 unions elected to do this year what the UAW and IAM are now contemplating. The mergers involved mostly small units. In all, about 119 unions and professional associations have gotten together in 69 mergers since the AFL-CIO merger of 1955.